Questions from General Calculus


Q: The boundaries of the shaded region are the y-axis,

The boundaries of the shaded region are the y-axis, the line y = 1, and the curve y = 4√x. Find the area of this region by writing x as a function of y and integrating with respect t...

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Q: Use the properties of integrals to verify that 2 < f-

Use the properties of integrals to verify that 2 < f-11 √1 + x2 dx < 2 √2

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Q: The current in a wire is defined as the derivative of the

The current in a wire is defined as the derivative of the charge: I (t) = Q'(t). (See Example 3 in Section 3.8.) What does fab I (t) dt represent?

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Q: Express the limit as a definite integral /

Express the limit as a definite integral

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Q: A honeybee population starts with 100 bees and increases at a rate

A honeybee population starts with 100 bees and increases at a rate of n'(t) bees per week. What does 100 + f015 n'(t) dt represent?

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Q: In Section 4.6 we defined the marginal revenue function R'

In Section 4.6 we defined the marginal revenue function R'(x) as the derivative of the revenue function R(x), where is the number of units sold. What does f10005000 R'(x) dx represent?

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Q: (a). Graph the epitrochoid with equations x = 11 cos

(a). Graph the epitrochoid with equations x = 11 cos t – 4 cos (11t/2), x = 11 sin t – 4 sin (11t/2) What parameter interval gives the complete curve? (b). Use your CAS to find the approximate length...

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Q: If f (x) is the slope of a trail at

If f (x) is the slope of a trail at a distance of x miles from the start of the trail, what does f35 f (x) dx represent?

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Q: Use Newton’s method to find all roots of the equation correct to

Use Newton’s method to find all roots of the equation correct to six decimal places. 1/x = 1 + x3

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Q: Use Newton’s method to find all the roots of the equation correct

Use Newton’s method to find all the roots of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.

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